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<span class="kw">let </span><font color="Maroon" title="c1">V</font> be   <a href="hilbert3.html#NM1" title="HILBERT3:NM.1">SetValuation</a>; <span class="comment"><font color="Red">:: according to </font></span><a class="ref" href="hilbert3.html#D7" target="_self" title="HILBERT3:def.7">HILBERT3:def 7</a> <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="Red">::  thesis: </font></span></a><span class="hide">  ex <font color="Olive" title="b1">x</font> being   <a href="hidden.html#M1" title="HIDDEN:mode.1">set</a>  st <br/>for <font color="Olive" title="b2">P</font> being   <a href="hilbert3.html#M1" title="HILBERT3:mode.1">Permutation</a> of <font color="Maroon" title="c1">V</font> holds  <font color="Olive" title="b1">x</font> <a href="abian.html#R1" title="ABIAN:pred.1">is_a_fixpoint_of</a>  <a href="hilbert3.html#K5" title="HILBERT3:func.5">Perm</a> <font color="Olive" title="b2">P</font>,<a href="hilbert1.html#K2" title="HILBERT1:func.2">VERUM</a> </span><br/>

<span class="kw">take </span>
 <a href="numbers.html#K6" title="NUMBERS:func.6">0</a> 
; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="Red">::  thesis: </font></span></a><span class="hide"> for <font color="Olive" title="b1">P</font> being   <a href="hilbert3.html#M1" title="HILBERT3:mode.1">Permutation</a> of <font color="Maroon" title="c1">V</font> holds   <a href="numbers.html#K6" title="NUMBERS:func.6">0</a>  <a href="abian.html#R1" title="ABIAN:pred.1">is_a_fixpoint_of</a>  <a href="hilbert3.html#K5" title="HILBERT3:func.5">Perm</a> <font color="Olive" title="b1">P</font>,<a href="hilbert1.html#K2" title="HILBERT1:func.2">VERUM</a> </span><br/>

<span class="kw">let </span><font color="Maroon" title="c2">P</font> be    <a href="hilbert3.html#M1" title="HILBERT3:mode.1">Permutation</a> of <font color="Maroon" title="c1">V</font>; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="Red">::  thesis: </font></span></a><span class="hide">  <a href="numbers.html#K6" title="NUMBERS:func.6">0</a>  <a href="abian.html#R1" title="ABIAN:pred.1">is_a_fixpoint_of</a>  <a href="hilbert3.html#K5" title="HILBERT3:func.5">Perm</a> <font color="Maroon" title="c2">P</font>,<a href="hilbert1.html#K2" title="HILBERT1:func.2">VERUM</a> </span><br/>

<a NAME="E1:51_1_1"/>
(  <a href="hilbert3.html#K3" title="HILBERT3:func.3">SetVal</a> <font color="Maroon" title="c1">V</font>,<a href="hilbert1.html#K2" title="HILBERT1:func.2">VERUM</a>  <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> 1 &amp;  <a href="numbers.html#K6" title="NUMBERS:func.6">0</a>  <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a> 1 )
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="hilbert3.html#D2" target="_self" title="HILBERT3:def.2">Def2</a>, <a class="ref" href="card_1.html#T87" title="CARD_1:th.87">CARD_1:87</a>, <a class="ref" href="tarski.html#D1" title="TARSKI:def.1">TARSKI:def 1</a></span>;<br/>
<span class="kw">hence </span><a NAME="E2:51_1_1"/>
 <a href="numbers.html#K6" title="NUMBERS:func.6">0</a>  <a href="abian.html#R1" title="ABIAN:pred.1">is_a_fixpoint_of</a>  <a href="hilbert3.html#K5" title="HILBERT3:func.5">Perm</a> <font color="Maroon" title="c2">P</font>,<a href="hilbert1.html#K2" title="HILBERT1:func.2">VERUM</a> 
 <span class="kw">by</span> <span class="lab"><a class="ref" href="hilbert3.html#T3" target="_self" title="HILBERT3:th.3">Th3</a>, <a class="ref" href="card_1.html#T87" title="CARD_1:th.87">CARD_1:87</a></span>; <a class="txt" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="Red">::  thesis: </font></span></a><span class="hide"> verum</span><br/>


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